Fraud and identity theft can be handled both in criminal and in civil court
. A complainant need not choose only one venue. In civil court, he can seek to be made financially whole and get damages as well, when appropriate. In criminal court, the state can punish the wrongdoer.
So yes, you can certaiinly try to get this person prosecuted. The way to do it is to go to the police and report the crime against you. Let them know you wish to have charges pressed.
Note that while this is a crime, sometimes when there is a contractual relationship between the two parties involved, the police will try to steer you to civil court. That's because the burden of proof is much more favorable to you in civil court than it is to the prosecutor in Criminal court. You would only have to demonstrate that you were defrauded more likely than not. The prosecutor on the other hand, would have to prove beyond a reasonable doubt.
If the police send you to civil court, your next step would be to go directly to the prosecutor and try to get charges pressed there. A prosecutor has complete discretion as to what cases he wishes to take on and how he proceeds with them, so does not have to agree with the police and can take the case on if he feels it's a good one that he can win.